When is it a good idea to keep strong students with strong students and weaker students with weaker students in the math classroom? And when is it beneficial to have a mixture of strengths within a collaborative group?

I'm interested to know what other literature exists on this subject, but personal perspectives are welcome as well.

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You seem to be asking about within-class grouping by ability, but there is a fair amount of literature about what happens when the entire class is grouped by ability, e.g., when mathematics classes for a certain year are divided into a standard version and an advanced version.

These "versions" are also called tracks, and the process of separating classes in this manner is known as tracking; analogously, the practice of removing the tracks and putting everyone into a single course is known as detracking.

Probably the effects that are witnessed with regard to tracking/detracking are the same sort you would see if you grouped by ability within-class, though perhaps the impact would be smaller in the latter case.

As for tracking/detracking literature: My first thoughts are an article by Loveless and another by Oakes.

Those two sources should get you started; look at their citations and the papers that cited them (especially the latter: see here) for further results. (The former paper is more casual, but gives a nice overall idea.)

Lastly: My general impression from the literature is that when you mix together students of different levels, the result is that the bottom and middle tier students do better, and the top tier students do slightly worse. The negative portion of this trade-off can probably be mitigated by paying some extra attention to the more advanced students and ensuring that they are sufficiently challenged (possibly by introducing supplementary materials). One of the consequences of top tier students not feeling challenged enough (addressed in the Loveless piece) is that their parents may wish to send them elsewhere; this can result in bright flight. As Loveless writes: "It's difficult to imagine how any school can benefit by alienating and driving out its best students" (p. 30).